Midterm Exam: Car Depreciation & Value Calculation

Hey guys! Let's dive into a classic math problem often found in midterm exams. This one focuses on the concept of depreciation, which is how the value of something, like a car, decreases over time. We'll break down the question step-by-step to make sure you totally get it. Understanding depreciation is super important, not just for exams, but also for real-life situations like figuring out the value of your own car or understanding investments. So, let's get started and make sure you ace this problem!

Understanding the Problem: Car Depreciation

Alright, so the core of the question is this: "A car is bought for Rp80,000,000. Each year, the resale value of the car becomes 19/20 of the previous year's price. What is the resale value of the car after three years?" The key here is the phrase "becomes 19/20." What this tells us is that the car's value decreases each year, and it decreases by a certain percentage. Instead of saying it decreases by a specific percentage, the problem states that the value retains 19/20 of its value each year. So, let's look at how we'll solve this. We're going to calculate the value of the car year by year. This is a common type of problem in math that shows up in various contexts, like finance and economics. The concept is pretty simple, but it's important to understand the math behind it to be able to apply the same concept to other problems that are similar in nature. Now, let's break down the calculations step by step, so that we understand exactly how this car's value is changing.

First, let's remember the initial price: Rp80,000,000. That's the starting point. At the end of the first year, the car's value will be 19/20 of the initial price. The second year, the car's value is 19/20 of the first year's value. We need to do this again for the third year, so we know what the resale value will be after the car has been used for three years. This kind of problem often appears in exams and tests. And the ability to understand and solve these kinds of problems, which often involve percentages or ratios, is really important for a well-rounded understanding of math. Keep in mind that a good grasp of basic arithmetic and the ability to think critically is all you need to solve this. Let's do this step by step.

We need to keep in mind, there are different ways of solving this problem. You could calculate the depreciation amount each year and subtract it, or you could use a formula directly. However, breaking it down year by year helps build a stronger understanding of the underlying principle. So, let's stick to doing this step by step. This method also makes it easier to spot any errors in the calculation. This will give us a very good way to understand the depreciation, which is a very important concept in business and finance. Let's start with the first year. After the first year, the car's value is (19/20) * Rp80,000,000.

Step-by-Step Calculation: Unveiling the Car's Value

Okay, guys, let's get our hands dirty with some calculations! We'll go year by year to keep things crystal clear. We're going to break it down, so it's super easy to follow. Don't worry, it's not as complex as it seems. Just some simple multiplication. And hey, even if you're not a math whiz, you can still totally nail this. Ready? Let's do this!

Year 1: The car's value after one year is (19/20) multiplied by the initial price (Rp80,000,000). So, it's (19/20) * 80,000,000 = Rp76,000,000. See? The car has already lost some value! So, the car now costs Rp76,000,000.

Year 2: Now we take the value from Year 1 (Rp76,000,000) and multiply it by 19/20 again. This gives us (19/20) * 76,000,000 = Rp72,200,000. The car's value has decreased again. The car now costs Rp72,200,000.

Year 3: Finally, we take the value from Year 2 (Rp72,200,000) and multiply it by 19/20 one last time. This equals (19/20) * 72,200,000 = Rp68,590,000. And there you have it! The car's value after three years is Rp68,590,000. So we have our final number.

By breaking it down this way, you can clearly see how the value decreases each year. This method allows us to build an intuition about this problem, making it easier to solve this type of problem. Also, this way is easier to understand and apply to other similar problems. Also, it becomes easy to check your answers. And remember, understanding the concept is more important than memorizing formulas, right?

The Answer and What It Means

So, after all that calculating, the answer is Rp68,590,000. This means the resale value of the car after three years of use is Rp68,590,000. Now, which of the provided answer options matches this value? You'll find that it's not one of the options given (a, b, c, or d). This highlights a crucial point: Always double-check your calculations and, if possible, the answer choices. There might have been a small error in the problem itself, but the process we used is correct. What's important is the process you used to find the solution. The steps we took, the way we thought about the problem – that's what matters. You can now confidently tackle similar depreciation problems.

This type of problem helps you understand how the value of an asset changes over time, considering various factors like wear and tear and market conditions. This is essential knowledge for anyone looking to buy, sell, or manage assets, including cars, real estate, or investments. Knowing how to calculate depreciation can help you make informed decisions and better understand the financial implications of your choices. So, while the exact answer might not match a given option, the skills you've gained are invaluable.

Key Takeaways and Next Steps

Alright, let's wrap things up with some key takeaways! First, depreciation problems are all about understanding how value decreases over time, whether it's a car, equipment, or anything else. Second, always pay close attention to the percentage or fraction by which the value decreases or retains each period. Third, breaking down the problem step by step can make it way easier to understand and avoid mistakes. So the most important things for the process are to understand the concept of depreciation, break down problems step by step, and pay close attention to the fraction or percentage that the car retains its value. Keep in mind that practice makes perfect, right? So, try similar problems, practice, and soon you'll be solving these with ease.

To solidify your understanding, try similar problems with different initial values, different depreciation rates, and different time periods. Also, explore how depreciation is used in business and finance – it's a super important concept. Keep practicing, and you'll be acing those exams in no time! Also, try to learn different methods to solve this kind of problems, like using an exponential formula. By doing this, you'll be able to solve these kinds of problems much faster. Finally, remember to always double-check your calculations and the answer choices. Keep it up, guys! You got this!